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# Classification: Applications of Subaperture Stitching Interferometry

According to the testing status of the subapertures, subaperture stitching interferometry can be categorized into three types: null subaperture stitching, nonnull subaperture stitching, and near-null subaperture stitching. Null stitching testing means that the test wavefront completely matches the nominal shape of the subaperture, and the subaperture is in a status of so-called null test, i.e., a null fringe will ideally be obtained. Typical cases of null stitching include stitching tests of large flats34 or planar wavefronts37,38,50 with a small interferometer, stitching tests of large convex spherical surfaces36 or spherical surfaces of high numerical aperture39 with a small spherical interferometer, stitching Hindle test of conic aspheres,51,52 or stitching test with null optics that is suitable for subapertures lying on the same ring with the same off-axis distance.40,53 Note that different aspheres or different rings demand different null optics. Figure 3 shows a combination of the Hindle test with the subaperture stitching interferometry applied to the conformal dome surface, which is a very steep ellipsoid. The focus of the TS and the center of curvature of the Hindle sphere coincide with the near focus and the far focus of the ellipsoid, respectively. Figure 4 shows a combination of the subaperture stitching interferometry with null optics, such

Figure 3 Stitching Hindle test of conformal dome surfaces.

as the aspheric test plate or computer-generated hologram (CGH), applied to the convex asphere.

A non-null stitching test means that the test wavefront does not match the nominal shape of the subaperture. The subaperture is in a status of non-null test, and a null fringe is unavailable even with ideal surfaces. To ensure that the interferometer can resolve the fringes, the aspheric departure of the subapertures must be within the dynamic range of the interferometer. This method is common when a spherical interferometer is used to test some aspheres with moderate departure. It does not need null optics and applies to different surface shapes. Compared with the full aperture, subaperture aberrations are reduced, which can ease the demands of null optics. However, subaperture aberrations of complex surfaces increase quickly with the off-axis distances. As a result, the stitching of steep aspheres requires a lot of subapertures to match the resolving capacity of the interferometer, which means low efficiency and low repeatability.43

Near-null subaperture stitching is proposed and expected to solve the above problem. In this case, most aberrations of subapertures at different locations are compensated to get a near-null test condition by variable aberrations generated by a variable null optics. The test wavefront does not completely match but mostly matches the shape of the subapertures. By flexibly compensating most aberrations at different locations of different surfaces, the number of interferometric fringes of every subaperture is small enough to be resolved. Note that the near-null test is inherently a non-null test, but we prefer this nomenclature to emphasize its feature of partially compensated aberrations. Near-null stitching

Figure 4 Stitching test of aspheres with null optics.

dramatically improves the flexibility to test large, steep complex surfaces. Typical near-null optics include the Risley prism pair adopted by QED Technologies26 and the Zernike phase-plate pair proposed by Chen et al.41

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